Exploring the ELI Measure
Exploring the ELI
eli_data <- clean_data_eli %>%
select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
analog_condition, itt_comp) %>%
unique() %>%
na.omit()
eli5_data <- clean_data_eli %>%
filter(eli_number %in% c("1", "2", "3", "4", "5")) %>%
select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
analog_condition, itt_comp) %>%
unique() %>%
na.omit() eli_wide_self <- clean_data_eli %>%
select(sub_id, eli_number, eli_self, pol_orient_1, pol_orient_2, pol_orient_3) %>%
unique() %>%
pivot_wider(names_from = eli_number, values_from = eli_self) %>%
rename("Politics: Overall" = pol_orient_1,
"Politics: Social" = pol_orient_2,
"Politics: Economic" = pol_orient_3,
"ElI 1" = `1`,
"ElI 2" = `2`,
"ElI 3" = `3`,
"ElI 4" = `4`,
"ElI 5" = `5`,
"ElI 6" = `6`,
"ElI 7" = `7`,
"ElI 8" = `8`,
"ElI 9" = `9`,
"ElI 10" = `10`)# These look the same as in the PSPB paper
hist(eli_wide_self$`ElI 1`)
hist(eli_wide_self$`ElI 2`)
hist(eli_wide_self$`ElI 3`)
hist(eli_wide_self$`ElI 4`)
hist(eli_wide_self$`ElI 5`)
Exploring relationship of ELI vars with each other and political orientation
Self
eli_self_cor <- eli_wide_self %>%
select(-sub_id)
eli_pol_cor <- cor(eli_self_cor)
corrplot(eli_pol_cor,
is.corr = TRUE,
#method = "number",
method = 'color',
tl.cex = .85,
tl.col = 'black',
addgrid.col = 'white',
addCoef.col = 'grey50')
Responses on the ELI are not related to responses on the political orientation questions nor each other (aka orthogonal)
Target
eli_wide_targ <- clean_data_eli %>%
select(sub_id, eli_number, eli_targ, pol_orient_1, pol_orient_2, pol_orient_3) %>%
unique() %>%
pivot_wider(names_from = eli_number, values_from = eli_targ) %>%
select(-sub_id) %>%
rename("Politics: Overall" = pol_orient_1,
"Politics: Social" = pol_orient_2,
"Politics: Economic" = pol_orient_3,
"ElI 1" = `1`,
"ElI 2" = `2`,
"ElI 3" = `3`,
"ElI 4" = `4`,
"ElI 5" = `5`,
"ElI 6" = `6`,
"ElI 7" = `7`,
"ElI 8" = `8`,
"ElI 9" = `9`,
"ElI 10" = `10`)
eli_targ_matrix_targ <- cor(eli_wide_targ)
corrplot(eli_targ_matrix_targ,
is.corr = TRUE,
#method = "number",
method = 'color',
tl.cex = .85,
tl.col = 'black',
addgrid.col = 'white',
addCoef.col = 'grey50')
The target has slightly higher correlations overall for the ELI, but lower ones in relation to political orientation
Stereo
eli_wide_stereo <- clean_data_eli %>%
select(sub_id, eli_number, eli_stereo, pol_orient_1, pol_orient_2, pol_orient_3) %>%
unique() %>%
pivot_wider(names_from = eli_number, values_from = eli_stereo) %>%
rename("Politics: Overall" = pol_orient_1,
"Politics: Social" = pol_orient_2,
"Politics: Economic" = pol_orient_3,
"ElI 1" = `1`,
"ElI 2" = `2`,
"ElI 3" = `3`,
"ElI 4" = `4`,
"ElI 5" = `5`,
"ElI 6" = `6`,
"ElI 7" = `7`,
"ElI 8" = `8`,
"ElI 9" = `9`,
"ElI 10" = `10`) %>%
select(-sub_id)
eli_stereo_matrix_stereo <- cor(eli_wide_stereo)
corrplot(eli_stereo_matrix_stereo,
is.corr = TRUE,
#method = "number",
method = 'color',
tl.cex = .85,
tl.col = 'black',
addgrid.col = 'white',
addCoef.col = 'grey50')
Again, higher correlations than for the self, but still only .35 as the highest. Low correlations with politics, but higher than with the target.
Exploring variance in intercepts for ELI
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html
Random intercept
With self
eli_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
(1 | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(eli_randint_test)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (1 | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12331.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0103 -0.5900 0.0054 0.6712 3.4945
##
## Random effects:
## Groups Name Variance
## sub_id (Intercept) 0.00000000000000000000000000000001469
## Residual 1.07012291677120230382058707618853077
## Std.Dev.
## 0.0000000000000001212
## 1.0344674556365716089
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.000000000000000006571 0.015886707663029700499 0.000
## eli_self_pmc 0.009365790070278842347 0.012313692726427382870 0.761
##
## Correlation of Fixed Effects:
## (Intr)
## eli_slf_pmc 0.000
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')The random variance for the intercept is 0, which is causing the singularity. This does not occur with the BFI. The data looks normal in the descriptives document. Checking some more stuff below.
Checking individual intercepts/slopes
Person mean centered variables
eli_coeffs_per_sub_c <- lmList(eli_targ_pmc ~ 1 + eli_self_pmc | sub_id, eli_data)
eli_coeffs_per_sub_c## Call:
## Model: eli_targ_pmc ~ 1 + eli_self_pmc | sub_id
## Data: eli_data
##
## Coefficients:
## (Intercept) eli_self_pmc
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##
## Degrees of freedom: 4240 total; 3392 residual
## Residual standard error: 1.05803Uncentered variables
eli_coeffs_per_sub <- lmList(eli_targ ~ 1 + eli_self | sub_id, eli_data)
eli_coeffs_per_sub## Call:
## Model: eli_targ ~ 1 + eli_self | sub_id
## Data: eli_data
##
## Coefficients:
## (Intercept) eli_self
## 1 4.0677966101694913447773 -0.271186440677966267287502
## 2 2.3281250000000000000000 0.132812499999999916733273
## 3 3.3214285714285707307170 -0.035714285714285698425385
## 4 2.7434944237918204024140 0.308550185873606108710732
## 5 2.7272727272727270708685 0.204545454545454530315141
## 6 2.2096069868995620311125 0.222707423580785879302368
## 8 4.8196721311475414495362 -0.491803278688524636574897
## 10 3.5692307692307680966337 -0.076923076923076788569134
## 11 1.0000000000000013322676 0.749999999999999777955395
## 12 2.7999999999999984900967 0.000000000000000219427092
## 13 3.0000000000000004440892 0.125000000000000083266727
## 14 3.5100671140939598835473 -0.026845637583892714012057
## 15 4.2483221476510060199416 -0.328859060402684477697477
## 16 2.0567375886524805750355 0.390070921985815610710802
## 17 2.9999999999999991118216 0.000000000000000052012348
## 19 4.1874999999999991118216 -0.562500000000000222044605
## 20 2.6714285714285712636240 0.142857142857142876968268
## 21 2.9999999999999960031971 0.000000000000000672553716
## 22 2.9999999999999991118216 -0.000000000000000024212645
## 23 2.9999999999999991118216 0.000000000000000000000000
## 25 4.1923076923076916244781 -0.192307692307692262856378
## 26 3.5140845070422530582732 -0.239436619718309706694725
## 27 3.6763485477178421412248 -0.265560165975103679159020
## 29 3.2173913043478266082786 0.072463768115941920577860
## 30 0.6938775510204090446464 0.693877551020408045445720
## 32 2.9999999999999991118216 -0.000000000000000084825507
## 33 3.8837209302325574888926 -0.124031007751938024408211
## 34 3.8993288590604020527053 -0.281879194630872520477283
## 35 3.4617940199335550666149 -0.109634551495016580036079
## 36 3.6666666666666674068153 -0.190476190476190937461709
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## 38 2.8859060402684550972197 0.073825503355704688579486
## 39 2.9285714285714274929262 0.132653061224489832170548
## 40 2.2758620689655177926625 0.206896551724137872652065
## 41 2.1562500000000000000000 0.218749999999999861222122
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## 59 2.9153439153439153486147 -0.005291005291005274231708
## 60 1.8529411764705878695736 0.401960784313725505434434
## 61 3.7209302325581399273347 -0.279069767441860572265711
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## 72 3.5961538461538458122391 -0.057692307692307667754683
## 73 2.7846889952153097702592 0.133971291866028574535363
## 74 6.0434782608695645222951 -0.956521739130434700548733
## 75 3.7796610169491526853847 -0.118644067796610297449433
## 76 5.0317460317460307450688 -0.349206349206349242475511
## 78 0.2690763052208833272516 0.714859437751004023198220
## 80 3.6000000000000005329071 -0.333333333333333481363070
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## 84 2.9999999999999986677324 0.000000000000000110143795
## 85 4.9830508474576271638057 -0.432203389830508433178125
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## 90 3.2837837837837828836030 -0.101351351351351537388723
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## 446 3.9999999999999995559108 0.000000000000000012906081
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## 448 3.1162790697674416229290 0.124031007751937982774848
## 449 3.0698689956331874917339 -0.196506550218340486635427
## 450 3.6937799043062198300902 -0.320574162679425900268626
## 451 0.9405405405405404817287 0.702702702702702963755144
## 452 4.0185185185185181566681 -0.435185185185185119394191
## 453 2.4999999999999995559108 0.235294117647058736997323
## 454 1.6285714285714276705619 0.591836734693877764001968
## 455 4.4658385093167689561255 -0.322981366459627328158177
## 456 2.9999999999999991118216 -0.000000000000000060473687
## 457 2.0737704918032782153148 0.163934426229508156680481
## 459 4.4999999999999991118216 -0.599999999999999977795540
## 460 0.8225806451612905911830 0.758064516129032139879484
## 461 1.9999999999999991118216 0.294117647058823594719001
## 462 4.6842105263157893801917 -0.526315789473684625399130
## 463 2.9545454545454550299155 -0.189393939393939392257238
## 464 4.4673913043478261641894 -0.402173913043478492568283
## 474 3.0571428571428564957557 0.214285714285714412596917
## 476 2.6538461538461537436717 0.096153846153846117550401
## 481 2.1000000000000000888178 0.249999999999999916733273
## 482 3.3057851239669422405143 -0.082644628099173611524009
## 483 4.6243093922651929972290 -0.303867403314917128298589
## 489 2.2318840579710137461689 0.202898550724637277697937
## 498 3.4054054054054048172873 0.027027027027027018118988
## 501 3.3521594684385385143344 -0.076411960132890408003981
## 508 3.7195121951219514144782 -0.060975609756097469416058
## 510 3.0745341614906820382203 0.068322981366459645258260
## 512 3.1063829787234040757937 0.028368794326241151410040
## 515 2.7999999999999993782751 0.142857142857142627168088
## 517 2.7173913043478261641894 0.108695652173912846172321
## 520 2.3119266055045870622564 0.330275229357798238982724
## 523 2.6410256410256409687065 0.128205128205128249252454
## 527 4.2375690607734801673701 -0.132596685082872922656350
## 530 2.6363636363636366866103 0.140495867768595072977433
## 536 5.3472222222222214327303 -0.513888888888888950567946
## 540 4.1666666666666660745477 -0.254901960784313763586084
##
## Degrees of freedom: 4240 total; 3392 residual
## Residual standard error: 1.05803There seems to be variability in the intercepts, even though lmer is not finding it.
Scatterplot of variables
ggplot(clean_data_eli, aes(eli_self_pmc, eli_targ_pmc)) +
geom_point()
Random intercept only
eli_randint_only <- lmer(eli_targ_pmc ~ 1 + # itt does not work as a RE; model does not converge
(1 | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(eli_randint_only)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ 1 + (1 | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12325
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9969 -0.5800 0.0000 0.6767 3.4802
##
## Random effects:
## Groups Name Variance
## sub_id (Intercept) 0.00000000000000000000000000000001469
## Residual 1.07001651332861880128177745064022020
## Std.Dev.
## 0.0000000000000001212
## 1.0344160252667293776
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.000000000000000006703 0.015885917827403422953 0
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')With only first five ELI items
These were the ones used in the PSPB paper
eli5_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
(1 | sub_id),
data = eli5_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(eli5_randint_test)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (1 | sub_id)
## Data: eli5_data
##
## REML criterion at convergence: 5708.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2955 -0.4688 -0.0294 0.6000 3.5763
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id (Intercept) 0.0000 0.0000
## Residual 0.8605 0.9276
## Number of obs: 2120, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.25528 0.02017 12.65
## eli_self_pmc -0.01700 0.01650 -1.03
##
## Correlation of Fixed Effects:
## (Intr)
## eli_slf_pmc -0.050
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Random Slopes/No random intercept
eli_randslopes_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
(0 + eli_self_pmc | sub_id),
data = eli_data)
summary(eli_randslopes_test)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (0 + eli_self_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12253.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0943 -0.5982 0.0068 0.6452 3.2360
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.04537 0.2130
## Residual 0.99461 0.9973
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.000000000000000005827 0.015315897842633369522 0.000
## eli_self_pmc 0.012234199608380517260 0.016068790172722027115 0.761
##
## Correlation of Fixed Effects:
## (Intr)
## eli_slf_pmc 0.000Running without the random intercept fixes the issue
Running models with random slopes/no intercepts
Threat composite
comp_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc + # itt does not work as a RE; model does not converge
(0 + eli_self_pmc | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(comp_eli_randslopes)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * itt_comp_gmc + (0 + eli_self_pmc |
## sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12233
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2229 -0.6049 0.0141 0.6519 3.1456
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.03695 0.1922
## Residual 0.99503 0.9975
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 0.00000000000000000569 0.01531913279267939354
## eli_self_pmc 0.01357934379323691258 0.01540005841078596720
## itt_comp_gmc 0.00000000000000001164 0.01430741929851506340
## eli_self_pmc:itt_comp_gmc -0.08568263438990457448 0.01433422509918278950
## t value
## (Intercept) 0.000
## eli_self_pmc 0.882
## itt_comp_gmc 0.000
## eli_self_pmc:itt_comp_gmc -5.977
##
## Correlation of Fixed Effects:
## (Intr) el_sl_ itt_c_
## eli_slf_pmc 0.000
## itt_cmp_gmc 0.000 0.000
## el_slf_p:__ 0.000 -0.017 0.000tab_model(comp_eli_randslopes,
digits = 3)| eli_targ_pmc | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.000 | -0.030 – 0.030 | 1.000 |
| eli self pmc | 0.014 | -0.017 – 0.044 | 0.378 |
| itt comp gmc | 0.000 | -0.028 – 0.028 | 1.000 |
|
eli self pmc * itt comp gmc |
-0.086 | -0.114 – -0.058 | <0.001 |
| Random Effects | |||
| σ2 | 1.00 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.04 | ||
| ρ01 | |||
| ρ01 | |||
| ICC | 0.06 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.013 / 0.071 | ||
Simple slopes
threat_levels = list(itt_comp_gmc = c(-1.07, 0.0, 1.07))
comp_simpslopes_eli <- emtrends(comp_eli_randslopes, ~ itt_comp_gmc,
var ="eli_self_pmc",
at = threat_levels)
comp_simpslopes_eli ## itt_comp_gmc eli_self_pmc.trend SE df asymp.LCL asymp.UCL
## -1.07 0.1053 0.0219 Inf 0.0623 0.1482
## 0.00 0.0136 0.0154 Inf -0.0166 0.0438
## 1.07 -0.0781 0.0215 Inf -0.1203 -0.0359
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95test(comp_simpslopes_eli)## itt_comp_gmc eli_self_pmc.trend SE df z.ratio p.value
## -1.07 0.1053 0.0219 Inf 4.802 <.0001
## 0.00 0.0136 0.0154 Inf 0.882 0.3779
## 1.07 -0.0781 0.0215 Inf -3.624 0.0003
##
## Degrees-of-freedom method: asymptoticpairs(comp_simpslopes_eli)## contrast estimate SE df z.ratio p.value
## (-1.07) - 0 0.0917 0.0153 Inf 5.977 <.0001
## (-1.07) - 1.07 0.1834 0.0307 Inf 5.977 <.0001
## 0 - 1.07 0.0917 0.0153 Inf 5.977 <.0001
##
## Degrees-of-freedom method: asymptotic
## P value adjustment: tukey method for comparing a family of 3 estimatesVisualization
comp_eli_maineffect <- effect("eli_self_pmc:itt_comp_gmc",
xlevels = list(itt_comp_gmc = c(-1.07, 0, 1.07)),
mod = comp_eli_randslopes)
comp_eli_maineffect <- as.data.frame(comp_eli_maineffect)
comp_eli_maineffect$itt_comp_gmc <- as.factor(comp_eli_maineffect$itt_comp_gmc)
ggplot(comp_eli_maineffect, aes(eli_self_pmc, fit, group = itt_comp_gmc)) +
geom_smooth(method = "lm",
size = .7,
se = FALSE,
colour = "black",
aes(linetype = itt_comp_gmc)) +
theme_minimal(base_size = 13) +
theme(legend.key.size = unit(1, "cm")) +
scale_linetype_manual("Target-level threat",
breaks = c(-1.07, 0, 1.07),
labels = c("Low",
"Average",
"High"),
values = c("solid",
"dashed",
"dotted")) +
labs(title = "Projection by target-level threat",
subtitle = "Using the ELI",
x = "ELI responses for self",
y = "ELI responses for target")
Assumptions
# checking normality of conditional residuals
qqnorm(residuals(comp_eli_randslopes), main="Q-Q plot for conditional residuals")
# checking the normality of the random effects (here random intercept):
qqnorm(ranef(comp_eli_randslopes)$sub_id$eli_self_pmc,
main="Q-Q plot for the self random effect")
plot_model(comp_eli_randslopes, type='diag')## [[1]]
##
## [[2]]
## [[2]]$sub_id
##
##
## [[3]]
##
## [[4]]
Also seems evenly spread but diagonal
Threat composite x target condition
compcond_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*target_condition + # itt does not work as a RE; model does not converge
(0 + eli_self_pmc | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(compcond_eli_randslopes)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * itt_comp_gmc * target_condition +
## (0 + eli_self_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12252.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2379 -0.6090 0.0184 0.6525 3.1815
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.03419 0.1849
## Residual 0.99598 0.9980
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate
## (Intercept) 0.000000000000000004358
## eli_self_pmc 0.088481139932443900187
## itt_comp_gmc 0.000000000000000008997
## target_conditionLOSS -0.000000000000000007145
## target_conditionWARM 0.000000000000000002538
## eli_self_pmc:itt_comp_gmc -0.049852936733676501968
## eli_self_pmc:target_conditionLOSS -0.118708640672557777518
## eli_self_pmc:target_conditionWARM -0.104016945472126712269
## itt_comp_gmc:target_conditionLOSS 0.000000000000000002307
## itt_comp_gmc:target_conditionWARM 0.000000000000000012476
## eli_self_pmc:itt_comp_gmc:target_conditionLOSS -0.053543741486550715247
## eli_self_pmc:itt_comp_gmc:target_conditionWARM 0.054026394796160101541
## Std. Error t value
## (Intercept) 0.041636752215280230238 0.000
## eli_self_pmc 0.040505094593943948011 2.184
## itt_comp_gmc 0.032985381665870824874 0.000
## target_conditionLOSS 0.057353512482594334876 0.000
## target_conditionWARM 0.051023008885615041275 0.000
## eli_self_pmc:itt_comp_gmc 0.032253424624806362186 -1.546
## eli_self_pmc:target_conditionLOSS 0.056651859972297845258 -2.095
## eli_self_pmc:target_conditionWARM 0.050034260083405897312 -2.079
## itt_comp_gmc:target_conditionLOSS 0.051791969957401644276 0.000
## itt_comp_gmc:target_conditionWARM 0.046193712076551797507 0.000
## eli_self_pmc:itt_comp_gmc:target_conditionLOSS 0.050683447925176337845 -1.056
## eli_self_pmc:itt_comp_gmc:target_conditionWARM 0.045640643166038177836 1.184
##
## Correlation of Fixed Effects:
## (Intr) el_sl_ itt_c_ t_LOSS t_WARM el__:__ e__:_L e__:_W i__:_L
## eli_slf_pmc 0.000
## itt_cmp_gmc 0.787 0.000
## trgt_cnLOSS -0.726 0.000 -0.571
## trgt_cnWARM -0.816 0.000 -0.642 0.592
## el_slf_p:__ 0.000 0.778 0.000 0.000 0.000
## el_s_:_LOSS 0.000 -0.715 0.000 0.000 0.000 -0.556
## el_s_:_WARM 0.000 -0.810 0.000 0.000 0.000 -0.630 0.579
## itt__:_LOSS -0.501 0.000 -0.637 -0.011 0.409 0.000 0.000 0.000
## itt__:_WARM -0.562 0.000 -0.714 0.408 0.273 0.000 0.000 0.000 0.455
## e__:__:_LOS 0.000 -0.495 0.000 0.000 0.000 -0.636 -0.034 0.401 0.000
## e__:__:_WAR 0.000 -0.550 0.000 0.000 0.000 -0.707 0.393 0.252 0.000
## i__:_W e__:__:_L
## eli_slf_pmc
## itt_cmp_gmc
## trgt_cnLOSS
## trgt_cnWARM
## el_slf_p:__
## el_s_:_LOSS
## el_s_:_WARM
## itt__:_LOSS
## itt__:_WARM
## e__:__:_LOS 0.000
## e__:__:_WAR 0.000 0.450tab_model(compcond_eli_randslopes,
digits = 3)| eli_targ_pmc | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.000 | -0.082 – 0.082 | 1.000 |
| eli self pmc | 0.088 | 0.009 – 0.168 | 0.029 |
| itt comp gmc | 0.000 | -0.065 – 0.065 | 1.000 |
| target condition [LOSS] | -0.000 | -0.112 – 0.112 | 1.000 |
| target condition [WARM] | 0.000 | -0.100 – 0.100 | 1.000 |
|
eli self pmc * itt comp gmc |
-0.050 | -0.113 – 0.013 | 0.122 |
|
eli self pmc * target condition [LOSS] |
-0.119 | -0.230 – -0.008 | 0.036 |
|
eli self pmc * target condition [WARM] |
-0.104 | -0.202 – -0.006 | 0.038 |
|
itt comp gmc * target condition [LOSS] |
0.000 | -0.102 – 0.102 | 1.000 |
|
itt comp gmc * target condition [WARM] |
0.000 | -0.091 – 0.091 | 1.000 |
|
(eli self pmc * itt comp gmc) * target condition [LOSS] |
-0.054 | -0.153 – 0.046 | 0.291 |
|
(eli self pmc * itt comp gmc) * target condition [WARM] |
0.054 | -0.035 – 0.144 | 0.237 |
| Random Effects | |||
| σ2 | 1.00 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.03 | ||
| ρ01 | |||
| ρ01 | |||
| ICC | 0.05 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.019 / 0.072 | ||
Simple Slopes
targ_levels <-list(target_condition = c("CONTROL", "LOSS", "WARM"))
simpslopes_eli_nostereo_compcond <- emtrends(compcond_eli_randslopes, ~ target_condition,
var ="eli_self_pmc",
at = targ_levels)
simpslopes_eli_nostereo_compcond ## target_condition eli_self_pmc.trend SE df asymp.LCL asymp.UCL
## CONTROL 0.0885 0.0405 Inf 0.00909 0.1679
## LOSS -0.0302 0.0396 Inf -0.10786 0.0474
## WARM -0.0155 0.0294 Inf -0.07311 0.0420
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95pairs(simpslopes_eli_nostereo_compcond)## contrast estimate SE df z.ratio p.value
## CONTROL - LOSS 0.1187 0.0567 Inf 2.095 0.0908
## CONTROL - WARM 0.1040 0.0500 Inf 2.079 0.0942
## LOSS - WARM -0.0147 0.0493 Inf -0.298 0.9522
##
## Degrees-of-freedom method: asymptotic
## P value adjustment: tukey method for comparing a family of 3 estimatestest(simpslopes_eli_nostereo_compcond)## target_condition eli_self_pmc.trend SE df z.ratio p.value
## CONTROL 0.0885 0.0405 Inf 2.184 0.0289
## LOSS -0.0302 0.0396 Inf -0.763 0.4454
## WARM -0.0155 0.0294 Inf -0.529 0.5969
##
## Degrees-of-freedom method: asymptoticAssumptions
# checking normality of conditional residuals
qqnorm(residuals(compcond_eli_randslopes), main="Q-Q plot for conditional residuals")
# checking the normality of the random effects
qqnorm(ranef(compcond_eli_randslopes)$sub_id$eli_self_pmc,
main="Q-Q plot for the self random effect")
plot_model(compcond_eli_randslopes, type='diag')## [[1]]
##
## [[2]]
## [[2]]$sub_id
##
##
## [[3]]
##
## [[4]]
Heavy tail?
Also seems evenly spread but diagonal
Visualization
no_stereo_viz <- eli_data %>%
mutate(target_condition = forcats::fct_relevel(target_condition, c("CONTROL", "WARM", "LOSS")))
target_labels <- c("CONTROL" = "Control",
"WARM" = "Warm",
"LOSS" = "Loss")
ggplot(no_stereo_viz, aes(eli_self_pmc, eli_targ_pmc, group = target_condition)) +
geom_smooth(method = "lm",
size = .7,
se = FALSE,
colour = "black",
aes(linetype = target_condition)) +
theme_minimal(base_size = 13) +
theme(legend.key.size = unit(1, "cm")) +
scale_linetype_manual("Target condition",
breaks = c("CONTROL", "WARM", "LOSS"),
labels = c("Control",
"Warm",
"Loss"),
values = c("solid",
"dashed",
"dotted")) +
labs(title = "Projection by target condition using the ELI",
subtitle = "Using raw data instead of model effects",
x = "ELI responses for self",
y = "ELI responses for target")
Analog x threat composite
analogcomp_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*itt_comp_gmc +
(0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcomp_eli_randslopes)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ ~ eli_self_pmc * analog_condition * itt_comp_gmc + (0 +
## eli_self_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12722.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.51750 -0.68352 -0.07376 0.76725 2.57997
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.0289 0.170
## Residual 1.1260 1.061
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.127608 0.023557 132.767
## eli_self_pmc 0.004498 0.022279 0.202
## analog_conditioncontrol 0.035595 0.032696 1.089
## itt_comp_gmc -0.118886 0.022344 -5.321
## eli_self_pmc:analog_conditioncontrol 0.020146 0.030791 0.654
## eli_self_pmc:itt_comp_gmc -0.059057 0.020877 -2.829
## analog_conditioncontrol:itt_comp_gmc 0.042211 0.030584 1.380
## eli_self_pmc:analog_conditioncontrol:itt_comp_gmc -0.051639 0.028680 -1.801
##
## Correlation of Fixed Effects:
## (Intr) el_sl_ anlg_c itt_c_ el__:_ e__:__ an_:__
## eli_slf_pmc 0.000
## anlg_cndtnc -0.721 0.000
## itt_cmp_gmc 0.073 0.000 -0.053
## el_slf_pm:_ 0.000 -0.724 0.000 0.000
## el_slf_p:__ 0.000 0.047 0.000 0.000 -0.034
## anlg_cnd:__ -0.053 0.000 0.007 -0.731 0.000 0.000
## el_sl_:_:__ 0.000 -0.034 0.000 0.000 -0.012 -0.728 0.000tab_model(analogcomp_eli_randslopes)| eli_targ | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 3.13 | 3.08 – 3.17 | <0.001 |
| eli self pmc | 0.00 | -0.04 – 0.05 | 0.840 |
|
analog condition [control] |
0.04 | -0.03 – 0.10 | 0.276 |
| itt comp gmc | -0.12 | -0.16 – -0.08 | <0.001 |
|
eli self pmc * analog condition [control] |
0.02 | -0.04 – 0.08 | 0.513 |
|
eli self pmc * itt comp gmc |
-0.06 | -0.10 – -0.02 | 0.005 |
|
analog condition [control] * itt comp gmc |
0.04 | -0.02 – 0.10 | 0.168 |
|
(eli self pmc * analog condition [control]) * itt comp gmc |
-0.05 | -0.11 – 0.00 | 0.072 |
| Random Effects | |||
| σ2 | 1.13 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.03 | ||
| ρ01 | |||
| ρ01 | |||
| ICC | 0.04 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.022 / 0.063 | ||
Analog x target condition
analogcond_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*target_condition +
(0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcond_eli_randslopes)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ ~ eli_self_pmc * analog_condition * target_condition +
## (0 + eli_self_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12695.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.46976 -0.62515 -0.04895 0.75378 2.64903
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.03014 0.1736
## Residual 1.11583 1.0563
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 3.3126761 0.0396434
## eli_self_pmc 0.1419875 0.0380866
## analog_conditioncontrol -0.0226761 0.0544646
## target_conditionLOSS -0.3439261 0.0575768
## target_conditionWARM -0.2010819 0.0564690
## eli_self_pmc:analog_conditioncontrol -0.0092576 0.0518635
## eli_self_pmc:target_conditionLOSS -0.2487041 0.0552807
## eli_self_pmc:target_conditionWARM -0.1654422 0.0538018
## analog_conditioncontrol:target_conditionLOSS -0.0007614 0.0803329
## analog_conditioncontrol:target_conditionWARM 0.1084503 0.0777930
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS 0.0120479 0.0762011
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM 0.0266920 0.0740320
## t value
## (Intercept) 83.562
## eli_self_pmc 3.728
## analog_conditioncontrol -0.416
## target_conditionLOSS -5.973
## target_conditionWARM -3.561
## eli_self_pmc:analog_conditioncontrol -0.178
## eli_self_pmc:target_conditionLOSS -4.499
## eli_self_pmc:target_conditionWARM -3.075
## analog_conditioncontrol:target_conditionLOSS -0.009
## analog_conditioncontrol:target_conditionWARM 1.394
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS 0.158
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM 0.361
##
## Correlation of Fixed Effects:
## (Intr) el_sl_ anlg_c t_LOSS t_WARM el__:_ e__:_L e__:_W a_:_LO
## eli_slf_pmc 0.000
## anlg_cndtnc -0.728 0.000
## trgt_cnLOSS -0.689 0.000 0.501
## trgt_cnWARM -0.702 0.000 0.511 0.483
## el_slf_pm:_ 0.000 -0.734 0.000 0.000 0.000
## el_s_:_LOSS 0.000 -0.689 0.000 0.000 0.000 0.506
## el_s_:_WARM 0.000 -0.708 0.000 0.000 0.000 0.520 0.488
## anlg_:_LOSS 0.493 0.000 -0.678 -0.717 -0.346 0.000 0.000 0.000
## anlg_:_WARM 0.510 0.000 -0.700 -0.351 -0.726 0.000 0.000 0.000 0.475
## e__:_:_LOSS 0.000 0.500 0.000 0.000 0.000 -0.681 -0.725 -0.354 0.000
## e__:_:_WARM 0.000 0.514 0.000 0.000 0.000 -0.701 -0.354 -0.727 0.000
## a_:_WA e__:_:_L
## eli_slf_pmc
## anlg_cndtnc
## trgt_cnLOSS
## trgt_cnWARM
## el_slf_pm:_
## el_s_:_LOSS
## el_s_:_WARM
## anlg_:_LOSS
## anlg_:_WARM
## e__:_:_LOSS 0.000
## e__:_:_WARM 0.000 0.477tab_model(analogcond_eli_randslopes)| eli_targ | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 3.31 | 3.23 – 3.39 | <0.001 |
| eli self pmc | 0.14 | 0.07 – 0.22 | <0.001 |
|
analog condition [control] |
-0.02 | -0.13 – 0.08 | 0.677 |
| target condition [LOSS] | -0.34 | -0.46 – -0.23 | <0.001 |
| target condition [WARM] | -0.20 | -0.31 – -0.09 | <0.001 |
|
eli self pmc * analog condition [control] |
-0.01 | -0.11 – 0.09 | 0.858 |
|
eli self pmc * target condition [LOSS] |
-0.25 | -0.36 – -0.14 | <0.001 |
|
eli self pmc * target condition [WARM] |
-0.17 | -0.27 – -0.06 | 0.002 |
|
analog condition [control] * target condition [LOSS] |
-0.00 | -0.16 – 0.16 | 0.992 |
|
analog condition [control] * target condition [WARM] |
0.11 | -0.04 – 0.26 | 0.163 |
|
(eli self pmc * analog condition [control]) * target condition [LOSS] |
0.01 | -0.14 – 0.16 | 0.874 |
|
(eli self pmc * analog condition [control]) * target condition [WARM] |
0.03 | -0.12 – 0.17 | 0.718 |
| Random Effects | |||
| σ2 | 1.12 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.03 | ||
| ρ01 | |||
| ρ01 | |||
| ICC | 0.04 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.031 / 0.072 | ||
Analog x threat composite x target condition
analogcompcond_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*target_condition*itt_comp_gmc +
(0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcompcond_eli_randslopes)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ ~ eli_self_pmc * analog_condition * target_condition *
## itt_comp_gmc + (0 + eli_self_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 12716.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.45864 -0.62278 -0.04065 0.74439 2.67835
##
## Random effects:
## Groups Name Variance Std.Dev.
## sub_id eli_self_pmc 0.02633 0.1623
## Residual 1.11580 1.0563
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate
## (Intercept) 3.270334
## eli_self_pmc 0.164799
## analog_conditioncontrol 0.074945
## target_conditionLOSS -0.265588
## target_conditionWARM -0.147308
## itt_comp_gmc -0.042857
## eli_self_pmc:analog_conditioncontrol -0.145364
## eli_self_pmc:target_conditionLOSS -0.237944
## eli_self_pmc:target_conditionWARM -0.194914
## analog_conditioncontrol:target_conditionLOSS -0.033859
## analog_conditioncontrol:target_conditionWARM -0.012297
## eli_self_pmc:itt_comp_gmc 0.023238
## analog_conditioncontrol:itt_comp_gmc 0.098220
## target_conditionLOSS:itt_comp_gmc -0.011096
## target_conditionWARM:itt_comp_gmc -0.024346
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS 0.235676
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM 0.197303
## eli_self_pmc:analog_conditioncontrol:itt_comp_gmc -0.140308
## eli_self_pmc:target_conditionLOSS:itt_comp_gmc -0.068673
## eli_self_pmc:target_conditionWARM:itt_comp_gmc 0.009972
## analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc -0.182028
## analog_conditioncontrol:target_conditionWARM:itt_comp_gmc -0.012837
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc 0.020668
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM:itt_comp_gmc 0.064131
## Std. Error
## (Intercept) 0.062646
## eli_self_pmc 0.058854
## analog_conditioncontrol 0.088192
## target_conditionLOSS 0.085502
## target_conditionWARM 0.074871
## itt_comp_gmc 0.049097
## eli_self_pmc:analog_conditioncontrol 0.080668
## eli_self_pmc:target_conditionLOSS 0.081249
## eli_self_pmc:target_conditionWARM 0.070077
## analog_conditioncontrol:target_conditionLOSS 0.121480
## analog_conditioncontrol:target_conditionWARM 0.110388
## eli_self_pmc:itt_comp_gmc 0.046165
## analog_conditioncontrol:itt_comp_gmc 0.069832
## target_conditionLOSS:itt_comp_gmc 0.078109
## target_conditionWARM:itt_comp_gmc 0.067990
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS 0.112743
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM 0.101900
## eli_self_pmc:analog_conditioncontrol:itt_comp_gmc 0.064158
## eli_self_pmc:target_conditionLOSS:itt_comp_gmc 0.071769
## eli_self_pmc:target_conditionWARM:itt_comp_gmc 0.063810
## analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc 0.109736
## analog_conditioncontrol:target_conditionWARM:itt_comp_gmc 0.100645
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc 0.100659
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM:itt_comp_gmc 0.093574
## t value
## (Intercept) 52.203
## eli_self_pmc 2.800
## analog_conditioncontrol 0.850
## target_conditionLOSS -3.106
## target_conditionWARM -1.967
## itt_comp_gmc -0.873
## eli_self_pmc:analog_conditioncontrol -1.802
## eli_self_pmc:target_conditionLOSS -2.929
## eli_self_pmc:target_conditionWARM -2.781
## analog_conditioncontrol:target_conditionLOSS -0.279
## analog_conditioncontrol:target_conditionWARM -0.111
## eli_self_pmc:itt_comp_gmc 0.503
## analog_conditioncontrol:itt_comp_gmc 1.407
## target_conditionLOSS:itt_comp_gmc -0.142
## target_conditionWARM:itt_comp_gmc -0.358
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS 2.090
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM 1.936
## eli_self_pmc:analog_conditioncontrol:itt_comp_gmc -2.187
## eli_self_pmc:target_conditionLOSS:itt_comp_gmc -0.957
## eli_self_pmc:target_conditionWARM:itt_comp_gmc 0.156
## analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc -1.659
## analog_conditioncontrol:target_conditionWARM:itt_comp_gmc -0.128
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS:itt_comp_gmc 0.205
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM:itt_comp_gmc 0.685tab_model(analogcompcond_eli_randslopes)| eli_targ | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 3.27 | 3.15 – 3.39 | <0.001 |
| eli self pmc | 0.16 | 0.05 – 0.28 | 0.005 |
|
analog condition [control] |
0.07 | -0.10 – 0.25 | 0.395 |
| target condition [LOSS] | -0.27 | -0.43 – -0.10 | 0.002 |
| target condition [WARM] | -0.15 | -0.29 – -0.00 | 0.049 |
| itt comp gmc | -0.04 | -0.14 – 0.05 | 0.383 |
|
eli self pmc * analog condition [control] |
-0.15 | -0.30 – 0.01 | 0.072 |
|
eli self pmc * target condition [LOSS] |
-0.24 | -0.40 – -0.08 | 0.003 |
|
eli self pmc * target condition [WARM] |
-0.19 | -0.33 – -0.06 | 0.005 |
|
analog condition [control] * target condition [LOSS] |
-0.03 | -0.27 – 0.20 | 0.780 |
|
analog condition [control] * target condition [WARM] |
-0.01 | -0.23 – 0.20 | 0.911 |
|
eli self pmc * itt comp gmc |
0.02 | -0.07 – 0.11 | 0.615 |
|
analog condition [control] * itt comp gmc |
0.10 | -0.04 – 0.24 | 0.160 |
|
target condition [LOSS] * itt comp gmc |
-0.01 | -0.16 – 0.14 | 0.887 |
|
target condition [WARM] * itt comp gmc |
-0.02 | -0.16 – 0.11 | 0.720 |
|
(eli self pmc * analog condition [control]) * target condition [LOSS] |
0.24 | 0.01 – 0.46 | 0.037 |
|
(eli self pmc * analog condition [control]) * target condition [WARM] |
0.20 | -0.00 – 0.40 | 0.053 |
|
(eli self pmc * analog condition [control]) * itt comp gmc |
-0.14 | -0.27 – -0.01 | 0.029 |
|
(eli self pmc * target condition [LOSS]) * itt comp gmc |
-0.07 | -0.21 – 0.07 | 0.339 |
|
(eli self pmc * target condition [WARM]) * itt comp gmc |
0.01 | -0.12 – 0.14 | 0.876 |
|
(analog condition [control] * target condition [LOSS]) * itt comp gmc |
-0.18 | -0.40 – 0.03 | 0.097 |
|
(analog condition [control] * target condition [WARM]) * itt comp gmc |
-0.01 | -0.21 – 0.18 | 0.899 |
|
(eli self pmc * analog condition [control] target condition [LOSS]) itt comp gmc |
0.02 | -0.18 – 0.22 | 0.837 |
|
(eli self pmc * analog condition [control] target condition [WARM]) itt comp gmc |
0.06 | -0.12 – 0.25 | 0.493 |
| Random Effects | |||
| σ2 | 1.12 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.03 | ||
| ρ01 | |||
| ρ01 | |||
| ICC | 0.04 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.039 / 0.075 | ||
The interaction significant in the 4-way is not in the 3-way model; it could be because of variance removed due to itt_comp… or it could be because the model is overfit/underpowered with this number of predictors. I’m not sure I trust ANY effect with analog perspective-taking
Correlation matrix (multicolinearity)
cor_predictors_eli <- clean_data_eli %>%
select(sub_id, eli_number, eli_self, eli_targ, itt_comp) %>%
unique() %>%
na.omit() %>%
select(eli_self, eli_targ, itt_comp) %>%
rename("ELI: Self" = eli_self,
"ELI: Target" = eli_targ,
"Threat Composite" = itt_comp)
cor_matrix_predictors_eli <- cor(cor_predictors_eli)
corrplot(cor_matrix_predictors_eli,
is.corr = TRUE,
#method = "number",
method = 'color',
tl.cex = .85,
tl.col = 'black',
addgrid.col = 'white',
addCoef.col = 'grey50')
Residual counter-projection with ELI
Threat composite
comp_eli_stereo <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*eli_stereo_pmc + # itt does not work as a RE; model does not converge
(0 + eli_self_pmc + eli_stereo_pmc | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(comp_eli_stereo)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * itt_comp_gmc * eli_stereo_pmc +
## (0 + eli_self_pmc + eli_stereo_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 11416.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6808 -0.5355 0.0171 0.5988 3.4913
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## sub_id eli_self_pmc 0.02599 0.1612
## eli_stereo_pmc 0.07400 0.2720 -0.01
## Residual 0.75865 0.8710
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.0011854 0.0134003 0.088
## eli_self_pmc 0.0275174 0.0136422 2.017
## itt_comp_gmc 0.0004259 0.0125165 0.034
## eli_stereo_pmc 0.2737683 0.0187626 14.591
## eli_self_pmc:itt_comp_gmc -0.0615540 0.0127172 -4.840
## eli_self_pmc:eli_stereo_pmc 0.0047924 0.0089489 0.536
## itt_comp_gmc:eli_stereo_pmc 0.1379914 0.0174409 7.912
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc 0.0120902 0.0081329 1.487
##
## Correlation of Fixed Effects:
## (Intr) el_sl_ itt_c_ el_st_ el_slf_pmc:t__ el_slf_pmc:l__ i__:__
## eli_slf_pmc 0.000
## itt_cmp_gmc 0.000 0.003
## eli_str_pmc -0.002 -0.012 0.000
## el_slf_pmc:t__ 0.003 -0.020 0.000 0.031
## el_slf_pmc:l__ -0.006 0.050 0.061 -0.004 -0.006
## itt_cmp_:__ 0.000 0.030 -0.002 -0.038 -0.012 -0.026
## el_s_:__:__ 0.060 -0.007 -0.005 -0.025 0.045 -0.097 -0.001tab_model(comp_eli_stereo,
digits = 3)| eli_targ_pmc | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.001 | -0.025 – 0.027 | 0.930 |
| eli self pmc | 0.028 | 0.001 – 0.054 | 0.044 |
| itt comp gmc | 0.000 | -0.024 – 0.025 | 0.973 |
| eli stereo pmc | 0.274 | 0.237 – 0.311 | <0.001 |
|
eli self pmc * itt comp gmc |
-0.062 | -0.086 – -0.037 | <0.001 |
|
eli self pmc * eli stereo pmc |
0.005 | -0.013 – 0.022 | 0.592 |
|
itt comp gmc * eli stereo pmc |
0.138 | 0.104 – 0.172 | <0.001 |
|
(eli self pmc * itt comp gmc) * eli stereo pmc |
0.012 | -0.004 – 0.028 | 0.137 |
| Random Effects | |||
| σ2 | 0.76 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.03 | ||
| τ11 sub_id.eli_stereo_pmc | 0.07 | ||
| ρ01 sub_id | -0.01 | ||
| ICC | 0.16 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.149 / 0.287 | ||
Simple slopes
comp_stereo_simpslopes_eli <- emtrends(comp_eli_stereo, ~ itt_comp_gmc,
var ="eli_self_pmc",
at = threat_levels)
comp_stereo_simpslopes_eli## itt_comp_gmc eli_self_pmc.trend SE df asymp.LCL asymp.UCL
## -1.07 0.0934 0.0195 Inf 0.055240 0.131520
## 0.00 0.0275 0.0136 Inf 0.000779 0.054256
## 1.07 -0.0383 0.0191 Inf -0.075732 -0.000958
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95test(comp_stereo_simpslopes_eli)## itt_comp_gmc eli_self_pmc.trend SE df z.ratio p.value
## -1.07 0.0934 0.0195 Inf 4.799 <.0001
## 0.00 0.0275 0.0136 Inf 2.017 0.0437
## 1.07 -0.0383 0.0191 Inf -2.010 0.0444
##
## Degrees-of-freedom method: asymptoticpairs(comp_stereo_simpslopes_eli)## contrast estimate SE df z.ratio p.value
## (-1.07) - 0 0.0659 0.0136 Inf 4.840 <.0001
## (-1.07) - 1.07 0.1317 0.0272 Inf 4.840 <.0001
## 0 - 1.07 0.0659 0.0136 Inf 4.840 <.0001
##
## Degrees-of-freedom method: asymptotic
## P value adjustment: tukey method for comparing a family of 3 estimatesVisualization
comp_stereo_eli_maineffect <- effect("eli_self_pmc:itt_comp_gmc",
xlevels = list(itt_comp_gmc = c(-1.07, 0, 1.07)),
mod = comp_eli_stereo)
comp_stereo_eli_maineffect <- as.data.frame(comp_stereo_eli_maineffect)
comp_stereo_eli_maineffect$itt_comp_gmc <- as.factor(comp_stereo_eli_maineffect$itt_comp_gmc)
ggplot(comp_stereo_eli_maineffect, aes(eli_self_pmc, fit, group = itt_comp_gmc)) +
geom_smooth(method = "lm",
size = .7,
se = FALSE,
colour = "black",
aes(linetype = itt_comp_gmc)) +
theme_minimal(base_size = 13) +
theme(legend.key.size = unit(1, "cm")) +
scale_linetype_manual("Target-level threat",
breaks = c(-1.07, 0, 1.07),
labels = c("Low",
"Average",
"High"),
values = c("solid",
"dashed",
"dotted")) +
labs(title = "Projection by target-level threat",
subtitle = "Using the ELI",
x = "ELI responses for self",
y = "ELI responses for target")
Assumptions
# checking normality of conditional residuals
qqnorm(residuals(comp_eli_stereo), main="Q-Q plot for conditional residuals")
# checking the normality of the random effects:
qqnorm(ranef(comp_eli_stereo)$sub_id$eli_self_pmc,
main="Q-Q plot for the self random effect")
# looking at random effect for stereo:
qqnorm(ranef(comp_eli_stereo)$sub_id$eli_stereo_pmc,
main="Q-Q plot for the self random effect")
plot_model(comp_eli_stereo, type='diag')## [[1]]
##
## [[2]]
## [[2]]$sub_id
##
##
## [[3]]
##
## [[4]]
Heavy tail and outliers?
Threat composite x targ condition
compcond_eli_stereo <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*eli_stereo_pmc*target_condition + # itt does not work as a RE; model does not converge
(0 + eli_self_pmc + eli_stereo_pmc | sub_id),
data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis
summary(compcond_eli_stereo)## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * itt_comp_gmc * eli_stereo_pmc *
## target_condition + (0 + eli_self_pmc + eli_stereo_pmc | sub_id)
## Data: eli_data
##
## REML criterion at convergence: 11425.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7121 -0.5415 0.0197 0.6013 3.3662
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## sub_id eli_self_pmc 0.02356 0.1535
## eli_stereo_pmc 0.06033 0.2456 0.14
## Residual 0.75930 0.8714
## Number of obs: 4240, groups: sub_id, 424
##
## Fixed effects:
## Estimate
## (Intercept) 0.0014845
## eli_self_pmc 0.1028476
## itt_comp_gmc 0.0005146
## eli_stereo_pmc 0.1359810
## target_conditionLOSS -0.0045587
## target_conditionWARM -0.0007657
## eli_self_pmc:itt_comp_gmc -0.0325643
## eli_self_pmc:eli_stereo_pmc 0.0068278
## itt_comp_gmc:eli_stereo_pmc 0.0584795
## eli_self_pmc:target_conditionLOSS -0.1626245
## eli_self_pmc:target_conditionWARM -0.1117977
## itt_comp_gmc:target_conditionLOSS 0.0065993
## itt_comp_gmc:target_conditionWARM -0.0010538
## eli_stereo_pmc:target_conditionLOSS 0.3385465
## eli_stereo_pmc:target_conditionWARM 0.1129196
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc 0.0138602
## eli_self_pmc:itt_comp_gmc:target_conditionLOSS 0.0076406
## eli_self_pmc:itt_comp_gmc:target_conditionWARM 0.0568879
## eli_self_pmc:eli_stereo_pmc:target_conditionLOSS 0.0173524
## eli_self_pmc:eli_stereo_pmc:target_conditionWARM -0.0111602
## itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS 0.0319973
## itt_comp_gmc:eli_stereo_pmc:target_conditionWARM -0.0168939
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS -0.0074514
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionWARM -0.0005625
## Std. Error
## (Intercept) 0.0364308
## eli_self_pmc 0.0358502
## itt_comp_gmc 0.0288578
## eli_stereo_pmc 0.0478002
## target_conditionLOSS 0.0508162
## target_conditionWARM 0.0446240
## eli_self_pmc:itt_comp_gmc 0.0285094
## eli_self_pmc:eli_stereo_pmc 0.0234383
## itt_comp_gmc:eli_stereo_pmc 0.0385392
## eli_self_pmc:target_conditionLOSS 0.0508035
## eli_self_pmc:target_conditionWARM 0.0442455
## itt_comp_gmc:target_conditionLOSS 0.0459587
## itt_comp_gmc:target_conditionWARM 0.0403926
## eli_stereo_pmc:target_conditionLOSS 0.0692498
## eli_stereo_pmc:target_conditionWARM 0.0587108
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc 0.0189388
## eli_self_pmc:itt_comp_gmc:target_conditionLOSS 0.0456204
## eli_self_pmc:itt_comp_gmc:target_conditionWARM 0.0403978
## eli_self_pmc:eli_stereo_pmc:target_conditionLOSS 0.0349865
## eli_self_pmc:eli_stereo_pmc:target_conditionWARM 0.0293039
## itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS 0.0625333
## itt_comp_gmc:eli_stereo_pmc:target_conditionWARM 0.0529115
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS 0.0304248
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionWARM 0.0264207
## t value
## (Intercept) 0.041
## eli_self_pmc 2.869
## itt_comp_gmc 0.018
## eli_stereo_pmc 2.845
## target_conditionLOSS -0.090
## target_conditionWARM -0.017
## eli_self_pmc:itt_comp_gmc -1.142
## eli_self_pmc:eli_stereo_pmc 0.291
## itt_comp_gmc:eli_stereo_pmc 1.517
## eli_self_pmc:target_conditionLOSS -3.201
## eli_self_pmc:target_conditionWARM -2.527
## itt_comp_gmc:target_conditionLOSS 0.144
## itt_comp_gmc:target_conditionWARM -0.026
## eli_stereo_pmc:target_conditionLOSS 4.889
## eli_stereo_pmc:target_conditionWARM 1.923
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc 0.732
## eli_self_pmc:itt_comp_gmc:target_conditionLOSS 0.167
## eli_self_pmc:itt_comp_gmc:target_conditionWARM 1.408
## eli_self_pmc:eli_stereo_pmc:target_conditionLOSS 0.496
## eli_self_pmc:eli_stereo_pmc:target_conditionWARM -0.381
## itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS 0.512
## itt_comp_gmc:eli_stereo_pmc:target_conditionWARM -0.319
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionLOSS -0.245
## eli_self_pmc:itt_comp_gmc:eli_stereo_pmc:target_conditionWARM -0.021tab_model(compcond_eli_stereo,
digits = 3)| eli_targ_pmc | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.001 | -0.070 – 0.073 | 0.967 |
| eli self pmc | 0.103 | 0.033 – 0.173 | 0.004 |
| itt comp gmc | 0.001 | -0.056 – 0.057 | 0.986 |
| eli stereo pmc | 0.136 | 0.042 – 0.230 | 0.004 |
| target condition [LOSS] | -0.005 | -0.104 – 0.095 | 0.929 |
| target condition [WARM] | -0.001 | -0.088 – 0.087 | 0.986 |
|
eli self pmc * itt comp gmc |
-0.033 | -0.088 – 0.023 | 0.253 |
|
eli self pmc * eli stereo pmc |
0.007 | -0.039 – 0.053 | 0.771 |
|
itt comp gmc * eli stereo pmc |
0.058 | -0.017 – 0.134 | 0.129 |
|
eli self pmc * target condition [LOSS] |
-0.163 | -0.262 – -0.063 | 0.001 |
|
eli self pmc * target condition [WARM] |
-0.112 | -0.199 – -0.025 | 0.012 |
|
itt comp gmc * target condition [LOSS] |
0.007 | -0.084 – 0.097 | 0.886 |
|
itt comp gmc * target condition [WARM] |
-0.001 | -0.080 – 0.078 | 0.979 |
|
eli stereo pmc * target condition [LOSS] |
0.339 | 0.203 – 0.474 | <0.001 |
|
eli stereo pmc * target condition [WARM] |
0.113 | -0.002 – 0.228 | 0.055 |
|
(eli self pmc * itt comp gmc) * eli stereo pmc |
0.014 | -0.023 – 0.051 | 0.464 |
|
(eli self pmc * itt comp gmc) * target condition [LOSS] |
0.008 | -0.082 – 0.097 | 0.867 |
|
(eli self pmc * itt comp gmc) * target condition [WARM] |
0.057 | -0.022 – 0.136 | 0.159 |
|
(eli self pmc * eli stereo pmc) * target condition [LOSS] |
0.017 | -0.051 – 0.086 | 0.620 |
|
(eli self pmc * eli stereo pmc) * target condition [WARM] |
-0.011 | -0.069 – 0.046 | 0.703 |
|
(itt comp gmc * eli stereo pmc) * target condition [LOSS] |
0.032 | -0.091 – 0.155 | 0.609 |
|
(itt comp gmc * eli stereo pmc) * target condition [WARM] |
-0.017 | -0.121 – 0.087 | 0.750 |
|
(eli self pmc * itt comp gmc * eli stereo pmc) * target condition [LOSS] |
-0.007 | -0.067 – 0.052 | 0.807 |
|
(eli self pmc * itt comp gmc * eli stereo pmc) * target condition [WARM] |
-0.001 | -0.052 – 0.051 | 0.983 |
| Random Effects | |||
| σ2 | 0.76 | ||
| τ00 | |||
| τ00 | |||
| τ11 sub_id.eli_self_pmc | 0.02 | ||
| τ11 sub_id.eli_stereo_pmc | 0.06 | ||
| ρ01 sub_id | 0.14 | ||
| ICC | 0.14 | ||
| N sub_id | 424 | ||
| Observations | 4240 | ||
| Marginal R2 / Conditional R2 | 0.173 / 0.288 | ||
Slight dip to the left but relatively spread, not funnel shape
Simple Slopes
simpslopes_eli_stereo_compcond <- emtrends(compcond_eli_stereo, ~ target_condition,
var ="eli_self_pmc",
at = targ_levels)
simpslopes_eli_stereo_compcond## target_condition eli_self_pmc.trend SE df asymp.LCL asymp.UCL
## CONTROL 0.10285 0.0359 Inf 0.0326 0.1731
## LOSS -0.05978 0.0360 Inf -0.1303 0.0108
## WARM -0.00895 0.0259 Inf -0.0598 0.0419
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95pairs(simpslopes_eli_stereo_compcond)## contrast estimate SE df z.ratio p.value
## CONTROL - LOSS 0.1626 0.0508 Inf 3.201 0.0039
## CONTROL - WARM 0.1118 0.0442 Inf 2.527 0.0309
## LOSS - WARM -0.0508 0.0444 Inf -1.146 0.4859
##
## Degrees-of-freedom method: asymptotic
## P value adjustment: tukey method for comparing a family of 3 estimatesVisualization
# interactions::interact_plot(compcond_eli_stereo, pred = eli_self_pmc, modx = itt_comp_gmc, mod2 = target_condition, interval = TRUE)
eli_stereo <- effect("eli_self_pmc:target_condition",
xlevels = list(target_condition = c("CONTROL",
"WARM",
"LOSS")),
mod = compcond_eli_stereo)
eli_stereo <- as.data.frame(eli_stereo)
eli_stereo$target_condition <- as.factor(eli_stereo$target_condition)
eli_stereo %<>%
mutate(target_condition = forcats::fct_relevel(target_condition, c("CONTROL", "WARM", "LOSS")))
target_labels <- c("CONTROL" = "Control",
"WARM" = "Warm",
"LOSS" = "Loss")
ggplot(eli_stereo, aes(eli_self_pmc, fit, group = target_condition)) +
geom_smooth(method = "lm",
size = .7,
se = FALSE,
colour = "black",
aes(linetype = target_condition)) +
theme_minimal(base_size = 13) +
theme(legend.key.size = unit(1, "cm")) +
facet_wrap(~target_condition,
labeller = labeller(target_condition = target_labels)) +
scale_linetype_manual("Threat composite",
breaks = c("-1.07", "0", "1.07"),
labels = c("Low",
"Average",
"High"),
values = c("solid",
"dashed",
"dotted")) +
labs(title = "Residual projection by target-level threat and target condition",
subtitle = "Using the ELI; Accounting for stereotyping",
x = "ELI responses for self",
y = "ELI responses for target")
Assumptions
# checking normality of conditional residuals
qqnorm(residuals(compcond_eli_stereo), main="Q-Q plot for conditional residuals")
# checking the normality of the random effects:
qqnorm(ranef(compcond_eli_stereo)$sub_id$eli_self_pmc,
main="Q-Q plot for the self random effect")
# looking at random effect for stereo:
qqnorm(ranef(compcond_eli_stereo)$sub_id$eli_stereo_pmc,
main="Q-Q plot for the self random effect")
plot_model(compcond_eli_stereo, type='diag')## [[1]]
##
## [[2]]
## [[2]]$sub_id
##
##
## [[3]]
##
## [[4]]
This may be starting to take on a funnel shape, but not so severe that I think I need to be concerned
---
title: "Exploring the ELI Measure"
output: 
    html_document:
      code_download: TRUE
      toc: TRUE
      toc_float:
        collapsed: FALSE
      toc_depth: 1
      code_folding: hide
editor_options: 
  chunk_output_type: console
---

```{r data prep, echo = FALSE, warning = FALSE, message = FALSE, error = FALSE}
# Loading packages
library(psych)
library(lme4)
library(nlme)
library(sjPlot)
library(effects)
library(magrittr) # part of the tidyverse but must be read in on its own
library(parameters)
library(dplyr)
library(tidyr)
library(rio)
library(ggplot2)
library(emmeans)
library(corrplot)
library(doParallel) 
library(doRNG)

# Functions to clean document, get data from wide to long format
source("functions/Cleaning.R")

# Setting global chunk options
knitr::opts_chunk$set(echo = TRUE,
                      message = FALSE,
                      warning = FALSE)

options(scipen = 999)

# Importing data
wide_data <- import("data/diss_main_combined_data_basic_clean.csv")

# wide_data_sub <- wide_data %>%
#   select(sub_id,
#          bfi_self_1:eli_self_10,
#          bfi_ster_1:eli_stereo_10,
#          bfi_targ_1:eli_targ_10)
# 
# bias_counts <- apply(wide_data_sub, 1, function(x) length(which(x=="3")))
# bias_counts <- as.data.frame(bias_counts)
# 
# total_answers <- length(wide_data_sub)
# 
# # Used the sub_ids obtained from below in function above
# bias_counts %>%
#   mutate(bias_percents = (bias_counts/total_answers)*100) %>%
#   filter(bias_percents > 50)
# 
# 
# wide_data <- wide_data[-c(12, 17, 18, 22, 24, 31, 40, 70, 78, 82, 86, 87, 99, 
#                           112, 130, 131, 144, 145, 147, 154, 165, 166, 180, 192, 
#                           216, 247, 253, 258, 265, 275, 291, 293, 313, 324, 349,
#                           362, 375, 385, 387, 409, 410, 460, 474, 483, 486), ] 

# Cleaning data using functions
long_data_eli <- get_wrangled_eli(wide_data)

clean_vars_eli <- get_vars_cleaned(long_data_eli)

clean_data_eli <- remove_participants(clean_vars_eli)

clean_data_eli %<>%    
  mutate(itt_comp = rowMeans(select(., c("realistic_q", "symbolic_q"))),
         itt_comp_gmc = scale(itt_comp, center = T, scale = F))
```

# Exploring the ELI

```{r}
eli_data <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
         target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
         analog_condition, itt_comp) %>% 
  unique() %>% 
  na.omit() 

eli5_data <- clean_data_eli %>% 
  filter(eli_number %in% c("1", "2", "3", "4", "5")) %>% 
  select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
         target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
         analog_condition, itt_comp) %>% 
  unique() %>% 
  na.omit() 
```

```{r}
eli_wide_self <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_self, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_self) %>% 
  rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`)
```

```{r}
# These look the same as in the PSPB paper
hist(eli_wide_self$`ElI 1`)
hist(eli_wide_self$`ElI 2`)
hist(eli_wide_self$`ElI 3`)
hist(eli_wide_self$`ElI 4`)
hist(eli_wide_self$`ElI 5`)
```


# Exploring relationship of ELI vars with each other and political orientation {.tabset .tabset-fade .tabset-pills}

## Self

```{r}
eli_self_cor <- eli_wide_self %>% 
  select(-sub_id)

eli_pol_cor <- cor(eli_self_cor)

corrplot(eli_pol_cor, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')
```

Responses on the ELI are not related to responses on the political orientation questions nor each other (aka orthogonal)

## Target

```{r}
eli_wide_targ <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_targ, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_targ) %>% 
  select(-sub_id) %>% 
   rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`)

eli_targ_matrix_targ <- cor(eli_wide_targ)

corrplot(eli_targ_matrix_targ, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')
```

The target has slightly higher correlations overall for the ELI, but lower ones in relation to political orientation

## Stereo

```{r}
eli_wide_stereo <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_stereo, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_stereo) %>% 
     rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`) %>% 
    select(-sub_id)

eli_stereo_matrix_stereo <- cor(eli_wide_stereo)

corrplot(eli_stereo_matrix_stereo, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')

```

Again, higher correlations than for the self, but still only .35 as the highest. Low correlations with politics, but higher than with the target.

# Exploring variance in intercepts for ELI

 https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html

## Random intercept

### With self

```{r}

eli_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli_randint_test)
```

The random variance for the intercept is 0, which is causing the singularity. This does not occur with the BFI. The data looks normal in the descriptives document. Checking some more stuff below.

### Checking individual intercepts/slopes

*Person mean centered variables*

```{r}
eli_coeffs_per_sub_c  <- lmList(eli_targ_pmc ~ 1 + eli_self_pmc | sub_id, eli_data)
eli_coeffs_per_sub_c
```

*Uncentered variables*

```{r}
eli_coeffs_per_sub  <- lmList(eli_targ ~ 1 + eli_self | sub_id, eli_data)
eli_coeffs_per_sub
```

There seems to be variability in the intercepts, even though lmer is not finding it.

### Scatterplot of variables

```{r}
ggplot(clean_data_eli, aes(eli_self_pmc, eli_targ_pmc)) +
  geom_point()
```

### Random intercept only

```{r}

eli_randint_only <- lmer(eli_targ_pmc ~ 1 + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli_randint_only)
```

## With only first five ELI items

These were the ones used in the PSPB paper

```{r}

eli5_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli5_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli5_randint_test)
```

## Random Slopes/No random intercept

```{r}
eli_randslopes_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) 


summary(eli_randslopes_test)
```

Running without the random intercept fixes the issue

# Running models with random slopes/no intercepts {.tabset .tabset-fade .tabset-pills}

## Threat composite 

```{r}
comp_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(comp_eli_randslopes)
tab_model(comp_eli_randslopes,
          digits = 3)
```

### Simple slopes

```{r}
threat_levels = list(itt_comp_gmc = c(-1.07, 0.0, 1.07))
comp_simpslopes_eli <- emtrends(comp_eli_randslopes, ~ itt_comp_gmc,
                              var ="eli_self_pmc",
                              at = threat_levels)

comp_simpslopes_eli 
test(comp_simpslopes_eli)
pairs(comp_simpslopes_eli)
```

### Visualization

```{r}
comp_eli_maineffect <- effect("eli_self_pmc:itt_comp_gmc",
                         xlevels = list(itt_comp_gmc = c(-1.07, 0, 1.07)),
                         mod = comp_eli_randslopes)

comp_eli_maineffect <- as.data.frame(comp_eli_maineffect)
comp_eli_maineffect$itt_comp_gmc <- as.factor(comp_eli_maineffect$itt_comp_gmc)

ggplot(comp_eli_maineffect, aes(eli_self_pmc, fit, group = itt_comp_gmc)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = itt_comp_gmc)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  scale_linetype_manual("Target-level threat",
                        breaks = c(-1.07, 0, 1.07), 
                       labels = c("Low",
                                  "Average",
                                  "High"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) +
    labs(title = "Projection by target-level threat",
         subtitle = "Using the ELI",
       x = "ELI responses for self",
       y = "ELI responses for target")
```

### Assumptions

```{r}
# checking normality of conditional residuals
qqnorm(residuals(comp_eli_randslopes), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects (here random intercept):
qqnorm(ranef(comp_eli_randslopes)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

plot_model(comp_eli_randslopes, type='diag')
```

Also seems evenly spread but diagonal

## Threat composite x target condition

```{r}
compcond_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*target_condition + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(compcond_eli_randslopes)
tab_model(compcond_eli_randslopes,
          digits = 3)
```

### Simple Slopes

```{r}
targ_levels <-list(target_condition = c("CONTROL", "LOSS", "WARM"))
simpslopes_eli_nostereo_compcond <- emtrends(compcond_eli_randslopes, ~ target_condition,
                              var ="eli_self_pmc",
                              at = targ_levels)


simpslopes_eli_nostereo_compcond 
pairs(simpslopes_eli_nostereo_compcond)
test(simpslopes_eli_nostereo_compcond)
```

### Assumptions

```{r}
# checking normality of conditional residuals
qqnorm(residuals(compcond_eli_randslopes), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects
qqnorm(ranef(compcond_eli_randslopes)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

plot_model(compcond_eli_randslopes, type='diag')
```

Heavy tail?

Also seems evenly spread but diagonal

### Visualization

```{r}


no_stereo_viz <- eli_data %>% 
  mutate(target_condition = forcats::fct_relevel(target_condition, c("CONTROL", "WARM", "LOSS")))

target_labels <- c("CONTROL" = "Control",
                   "WARM" = "Warm",
                   "LOSS" = "Loss")

ggplot(no_stereo_viz, aes(eli_self_pmc, eli_targ_pmc, group = target_condition)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = target_condition)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  scale_linetype_manual("Target condition",
                        breaks = c("CONTROL", "WARM", "LOSS"), 
                       labels = c("Control",
                                  "Warm",
                                  "Loss"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) +
    labs(title = "Projection by target condition using the ELI",
         subtitle = "Using raw data instead of model effects",
       x = "ELI responses for self",
       y = "ELI responses for target")
```

## Analog x threat composite

```{r}
analogcomp_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*itt_comp_gmc +
       (0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcomp_eli_randslopes)

tab_model(analogcomp_eli_randslopes)
```

## Analog x target condition

```{r}
analogcond_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*target_condition +
       (0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcond_eli_randslopes)

tab_model(analogcond_eli_randslopes)
```

## Analog x threat composite x target condition

```{r}
analogcompcond_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*target_condition*itt_comp_gmc +
       (0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcompcond_eli_randslopes)

tab_model(analogcompcond_eli_randslopes)
```

The interaction significant in the 4-way is not in the 3-way model; it could be because of variance removed due to itt_comp... or it could be because the model is overfit/underpowered with this number of predictors. I'm not sure I trust ANY effect with analog perspective-taking

# Correlation matrix (multicolinearity) {.tabset .tabset-fade .tabset-pills}

```{r}
cor_predictors_eli <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_self, eli_targ, itt_comp) %>% 
  unique() %>% 
  na.omit() %>% 
  select(eli_self, eli_targ, itt_comp) %>% 
  rename("ELI: Self" = eli_self,
         "ELI: Target" = eli_targ,
         "Threat Composite" = itt_comp)

cor_matrix_predictors_eli <- cor(cor_predictors_eli)

corrplot(cor_matrix_predictors_eli, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')
```

# Residual counter-projection with ELI {.tabset .tabset-fade .tabset-pills}

## Threat composite

```{r}
comp_eli_stereo <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*eli_stereo_pmc + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc + eli_stereo_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(comp_eli_stereo)
tab_model(comp_eli_stereo,
          digits = 3)
```

### Simple slopes

```{r}
comp_stereo_simpslopes_eli <- emtrends(comp_eli_stereo, ~ itt_comp_gmc,
                              var ="eli_self_pmc",
                              at = threat_levels)

comp_stereo_simpslopes_eli
test(comp_stereo_simpslopes_eli)
pairs(comp_stereo_simpslopes_eli)
```

### Visualization

```{r}
comp_stereo_eli_maineffect <- effect("eli_self_pmc:itt_comp_gmc",
                         xlevels = list(itt_comp_gmc = c(-1.07, 0, 1.07)),
                         mod = comp_eli_stereo)

comp_stereo_eli_maineffect <- as.data.frame(comp_stereo_eli_maineffect)
comp_stereo_eli_maineffect$itt_comp_gmc <- as.factor(comp_stereo_eli_maineffect$itt_comp_gmc)

ggplot(comp_stereo_eli_maineffect, aes(eli_self_pmc, fit, group = itt_comp_gmc)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = itt_comp_gmc)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  scale_linetype_manual("Target-level threat",
                        breaks = c(-1.07, 0, 1.07), 
                       labels = c("Low",
                                  "Average",
                                  "High"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) +
    labs(title = "Projection by target-level threat",
         subtitle = "Using the ELI",
       x = "ELI responses for self",
       y = "ELI responses for target")
```

### Assumptions

```{r}
# checking normality of conditional residuals
qqnorm(residuals(comp_eli_stereo), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects:
qqnorm(ranef(comp_eli_stereo)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

# looking at random effect for stereo:
qqnorm(ranef(comp_eli_stereo)$sub_id$eli_stereo_pmc,
       main="Q-Q plot for the self random effect")

plot_model(comp_eli_stereo, type='diag')
```

Heavy tail and outliers?

## Threat composite x targ condition

```{r}
compcond_eli_stereo <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc*eli_stereo_pmc*target_condition + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc + eli_stereo_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(compcond_eli_stereo)
tab_model(compcond_eli_stereo,
          digits = 3)
```

Slight dip to the left but relatively spread, not funnel shape

### Simple Slopes

```{r}
simpslopes_eli_stereo_compcond <- emtrends(compcond_eli_stereo, ~ target_condition,
                              var ="eli_self_pmc",
                              at = targ_levels)


simpslopes_eli_stereo_compcond
pairs(simpslopes_eli_stereo_compcond)
```

### Visualization

```{r}

# interactions::interact_plot(compcond_eli_stereo, pred = eli_self_pmc, modx = itt_comp_gmc, mod2 = target_condition, interval = TRUE)

eli_stereo <- effect("eli_self_pmc:target_condition",
                         xlevels = list(target_condition = c("CONTROL",
                                                             "WARM",
                                                             "LOSS")),
                         mod = compcond_eli_stereo)

eli_stereo <- as.data.frame(eli_stereo)
eli_stereo$target_condition <- as.factor(eli_stereo$target_condition)

eli_stereo %<>% 
  mutate(target_condition = forcats::fct_relevel(target_condition, c("CONTROL", "WARM", "LOSS")))

target_labels <- c("CONTROL" = "Control",
                   "WARM" = "Warm",
                   "LOSS" = "Loss")

ggplot(eli_stereo, aes(eli_self_pmc, fit, group = target_condition)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = target_condition)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  facet_wrap(~target_condition,
             labeller = labeller(target_condition = target_labels)) +
  scale_linetype_manual("Threat composite",
                        breaks = c("-1.07", "0", "1.07"), 
                       labels = c("Low",
                                  "Average",
                                  "High"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) +
    labs(title = "Residual projection by target-level threat and target condition",
         subtitle = "Using the ELI; Accounting for stereotyping",
       x = "ELI responses for self",
       y = "ELI responses for target")
```

### Assumptions

```{r}
# checking normality of conditional residuals
qqnorm(residuals(compcond_eli_stereo), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects:
qqnorm(ranef(compcond_eli_stereo)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

# looking at random effect for stereo:
qqnorm(ranef(compcond_eli_stereo)$sub_id$eli_stereo_pmc,
       main="Q-Q plot for the self random effect")

plot_model(compcond_eli_stereo, type='diag')
```

This may be starting to take on a funnel shape, but not so severe that I think I need to be concerned

